Abstract
The polynomial of a graph is the characteristic polynomial of its 0–1 adjacency matrix. Two graphs are cospectral if their polynomials are the same.
In this paper some of the results from a numerical study of the polynomials of graphs are presented. The study has encompassed 9 point graphs, 9 point bipartite graphs, 14 point trees and 13 point forests. Also given are several theoretical results which were prompted by the numerical data. These include two characterizations of those cospectral graphs which have cospectral complements, and a proof that, in the sense of Schwenk [20] "almost no" trees are characterized by their polynomials together with the polynomials of their complements. In addition, mention is made of those cospectral graphs which have cospectral linegraphs, and those which are cospectral to their own complements.
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© 1976 Springer-Verlag
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Godsil, C., Mckay, B. (1976). Some computational results on the spectra of graphs. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097370
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DOI: https://doi.org/10.1007/BFb0097370
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